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Second degree moments – a tool for the f ault p lane d etection?

Second degree moments – a tool for the f ault p lane d etection?. Petra Adamo vá Jan Šílený. Geophysical Institute, Academy of Sciences, Prague, Czech Republic e-mail: adamova@ig.cas.cz. Introduction to second degree moments. Standard moment tensor Point source: couple of planes.

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Second degree moments – a tool for the f ault p lane d etection?

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  1. Second degreemoments – atool for the fault planedetection? Petra Adamová Jan Šílený Geophysical Institute, Academy of Sciences, Prague, Czech Republic e-mail: adamova@ig.cas.cz

  2. Introduction to second degree moments Standard moment tensor Point source: couple of planes

  3. Introduction to second degree moments “Finite source” parameters from point source approximation • traditional modeling of slip on fault plane is costly and data are not available (no stations near the fault) • 2nd degree moments are advantageous alternative • geometry of the source • duration of the source process • spatial and temporal centroid • rupture velocity vector

  4. Theory Zero degree moment tensor (standard MT) Second degree moments, Doornbos (1982) Temporal centroid Spatial centroid Rupture propagation Source process duration Source ellipsoid

  5. Inverse scheme: full waveform inversion Standard MT Estimation of first and second degree moments exclusion of the non-physical solutions  inversion is faster

  6. Interpretation of second degree moments Centroid Rupture propagation vector Source ellipsoid

  7. Detection of the fault plane Moment tensor (DC part)  couple of planes (fault and auxiliary)  ambiguity 2nd degree moments  source ellipsoid (volume of the focus) Removing of the ambiguity: Plane containing the source ellipsoid (large axis)  fault plane Convenient geometry Inconvenient geometry

  8. Ridgeway Mine, Australia Seismicity in December2009 (ISS International) Malovichko, D. [2010] Ridgeway. Routine estimation of the source mechanisms: December 2009. ISSI Document Number: ISSREP_RWM_MECHANISMS200912.

  9. Location of selected events 2 5 3 4 2 1 5 3 4 1 Location of 5 events from Ridgeway mine from December 2009

  10. Moment tensor solution2009 Dec 0407:35:06, M = 2.1 IMS solution (spectral amplitudes) P and S wave amplitude inversion Full waveform inversion Frequency range 5 - 25 Hz

  11. Second degree moments (1)2009 Dec0407:35:06, M = 2.1 Source ellipsoid 3-D view

  12. Second degree moments (2)2009 Dec0407:35:06, M = 2.1 Temporal centroid = 0.01 sec Duration of the source process = 0.1 sec Average rupture velocity 2.0 km/s H – hypocenter C – spatial centroid position

  13. Moment tensor solution2009 Dec 04 03:19:07M = 1.3 DC = 32 % CLVD = 23 % ISO = 46 % IMS solution (spectral amplitudes) P wave amplitude inversion DC = 38 % CLVD = 25 % ISO = 37 % Full waveform inversion Frequency range 5 - 30 Hz (Corner frequency ~ 35 Hz)

  14. Second degree moments2009 Dec 04 03:19:07M = 1.3 Temporal centroid = 0.025 sec Duration of the source process = 0.15 sec Average rupture velocity 1.8 km/s Inconvenient geometry for estimation of the remaining parameters: source ellipsoid and rupture velocity vector lie on the intersection of 2 nodal planes We estimated second degree moments successfully but we cannot recognize which plane is the fault plane

  15. Jack-knife test, event 3 Removing one or 2 stations from the data set All jack-knife trials All jack-knife trials except removal of stations 25 and 39

  16. Jack-knife test, second degree moments Temporal centroid 0.01 sec For all jack-knife trials Source duration 0.1 sec nearly the same values Rupture velocity 2.1 km/sec Spatial centroid 1 m NS, 1 m EW, -10 m Z from the hypocenter Source ellipsoid Fault orientation Gray ellipsoid: inversion from all stations Dashed ellipsoids: jack-knife trials with extreme deviations

  17. Standard MT for selected events Fault plane

  18. Source ellipsoids • Removal of ambiguity of the two nodal planes • Correlation with geological faults

  19. Conclusions • standard moment tensor: dot • second degree moments: beyond dot: • estimate of source shape, rupture propagation vector, … • second degree moments bring additional information to standard MT: source ellipsoid, duration of the source process, average rupture velocity • a chance to remove ambiguity of the two nodal planes

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